The almost cyclicity of the fundamental groups of positively curved manifolds |
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Authors: | Xiaochun Rong |
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Institution: | (1) Mathematics Department, University of Chicago, Chicago, IL 60637, USA; e-mail: xr@math.uchicago.edu, US |
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Abstract: | Recall that a pure F-structure is a kind of generalized torus action. The main result asserts that if a compact positively
curved manifold M
n
admits an invariant pure F-structure such that each orbit has positive dimension, then the fundamental group has a finite
cyclic subgroup with index less than w
n
, a constant depending only on n. As an application, we conclude that for all 0<δ≦1, the fundamental group of a δ-pinched n-manifold either has a cyclic subgroup with index less than w
n
or has order less than w(n,δ), a constant depending only on n and δ. In particular, this substantially improves the main result inRo1].
Oblatum 1-IX-1995 & 26-I-1996 |
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Keywords: | |
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